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Real-world optimization problems often have expensive objective functions interms of cost and time. It is desirable to find near-optimal solutions withvery few function evaluations. Surrogate-assisted optimizers tend to reduce therequired number of function evaluations by replacing the real function with anefficient mathematical model built on few evaluated points. Problems with ahigh condition number are a challenge for many surrogate-assisted optimizersincluding SACOBRA. To address such problems we propose a new online whiteningoperating in the black-box optimization paradigm. We show on a set ofhigh-conditioning functions that online whitening tackles SACOBRA's earlystagnation issue and reduces the optimization error by a factor between 10 to1e12 as compared to the plain SACOBRA, though it imposes many extra functionevaluations. Covariance matrix adaptation evolution strategy (CMA-ES) has forvery high numbers of function evaluations even lower errors, whereas SACOBRAperforms better in the expensive setting (less than 1e03 function evaluations).If we count all parallelizable function evaluations (population evaluation inCMA-ES, online whitening in our approach) as one iteration, then bothalgorithms have comparable strength even on the long run. This holds forproblems with dimension D <= 20.

SACOBRA with Online Whitening for Solving Optimization Problems with High Conditioning